The purpose of the present article is to derive some subordination and superordina-tion results for certain normalized analytic functions involving fractional integral operator. More-over, this result is applied to find a relation between univalent solutions for fractional differentialequation.Full textAcknowledgement. The work presented here was supported by eScienceFund<lb...

the purpose of this present paper is to derive some subordination and superordination results for certain analytic functions in the open unit disk. relevant connections of the results, which are presented in the paper, with various known results are also considered.

in present paper acertain convolution operator of analytic functions is defined.moreover, subordination- and superordination- preserving propertiesfor a class of analytic operators defined on the space of normalizedanalytic functions in the open unit disk is obtained. we also applythis to obtain sandwich results and generalizations of some knownresults.

If H(U) denotes the space of analytic functions in the unit disk U, for the integral operator Aα,β,γ,δ : K → H(U), with K ⊂ H(U), defined by Aα,β,γ,δ[f ](z) = [ β + γ zγ ∫ z 0 f(t)h(t)t d t ]1/β , ( α, β, γ, δ ∈ C and h ∈ H(U) ) , we will determine sufficient conditions on g1, g2, α, β and γ such that zh(z) [ g1(z) z ]α ≺ zh(z) [ f(z) z ]α ≺ zh(z) [ g2(z) z ]α

The purpose of this present paper is to derive some subordination and superordination results for certain analytic functions in the open unit disk. Relevant connections of the results, which are presented in the paper, with various known results are also considered.

Let A denote the class of analytic functions in the open unit disk U = {z : |z| < 1} normalized by f(0) = f ′(0) − 1 = 0. In this paper, we introduce and study certain subclasses of analytic functions. Several inclusion relations of various subclasses of analytic functions, coefficient estimates , growth and distortion theorems, Hadamard Product, extreme points, integral means and inclusion pro...

in the present paper, we prove subordination, superordination and sandwich-type properties of a certain integral operators for univalent functions on open unit disc, moreover the special behavior of this class is investigated.